What are the x- and y-intercepts of the quadratic equation y = (x - 1)2 - 16? Identify the x-intercepts by graphing the quadratic equation.

Question

whpalmer4 · Answer

the y-intercept is just the value of the equation at x = 0.  Plug x=0 into the formula and evaluate it.

The x-intercepts are the values of x such that y = 0.  Set y =0 and solve for $x$ via factoring, completing the square, quadratic formula, or graphing (the latter being the requested method here, but you can check your work with one of the others).

whpalmer4 · Answer

You could also solve this by observing that for $y = 0$, $(x-1)^2 = 16$, take the square root of both sides, and solve for $x$.  Note that you have to take both the positive and negative values of the square root of 16 because this is a quadratic and all quadratics have exactly two solutions (which may be identical, but there are two of them, nonetheless).